Abstract

We extend the formalisms developed in Gair et al. [1] and Cornish and van Haasteren [2] to create
maps of gravitational-wave backgrounds using a network of ground-based laser interferometers. We
show that in contrast to pulsar timing arrays, which are insensitive to half of the gravitational-wave
sky (the curl modes), a network of ground-based interferometers is sensitive to both the gradient
and curl components of the background. The spatial separation of a network of interferometers,
or of a single interferometer at di erent times during its rotational and orbital motion around the
Sun, allows for recovery of both components. We derive expressions for the response functions of a
laser interferometer in the small-antenna limit, and use these expressions to calculate the overlap
reduction function for a pair of interferometers. We also construct maximum-likelihood estimates of
the + and -polarization modes of the gravitational-wave sky in terms of the response matrix for a
network of ground-based interferometers, evaluated at discrete times during Earth's rotational and
orbital motion around the Sun. We demonstrate the feasibility of this approach for some simple
simulated backgrounds (a single point source and spatially-extended distributions having only grad
or curl components), calculating maximum-likelihood sky maps and uncertainty maps based on
the (pseudo)inverse of the response matrix. The distinction between this approach and standard
methods for mapping gravitational-wave power is also discussed

Published 18 August 2015.
J. D. R. acknowledges support from National Science
Foundation Awards No. PHY-1205585 and No. CREST
HRD-1242090. This research was in part supported by
S. T.’s appointment to the NASA Postdoctoral Program at
the Jet Propulsion Laboratory, administered by Oak Ridge
Associated Universities through a contract with NASA.
N. J. C. acknowledges support from National Science
Foundation Award No. PHY-1306702 and the
NANOGrav Physics Frontier Center, Award No. NSF
PFC-1430284. J. G.’s work is supported by the Royal
Society. C. M. F. M.’s work is supported by a Marie
Curie International Outgoing Fellowship within the 7th
European Community Framework Programme. R. v. H.
acknowledges support by NASA through Einstein
Fellowship Grant No. PF3-140116. J. D. R. thanks Malik
Rakhmanov for useful discussions regarding pseudoinverse
calculations when the system of equations is underdetermined.
This research has made use of PYTHON and its
standard libraries: NUMPY and MATPLOTLIB. We have also
made use of MEALPIX (MATLAB implementation of HEALPix
[28]), developed by the GWAstro Research Group and
available from http://gwastro.psu.edu. This work was
performed using the Darwin Supercomputer of the
University of Cambridge High Performance Computing
Service (http://www.hpc.cam.ac.uk/), provided by Dell Inc.
using Strategic Research Infrastructure Funding from the
Higher Education Funding Council for England and
funding from the Science and Technology Facilities
Council. This paper has been assigned LIGO DCC
No. LIGO-P1500065.